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%I #54 Aug 26 2021 08:54:06
%S 1,2,3,4,5,6,7,8,9,10,12,21,23,32,34,43,45,54,56,65,67,76,78,87,89,98,
%T 101,121,123,210,212,232,234,321,323,343,345,432,434,454,456,543,545,
%U 565,567,654,656,676,678,765,767,787,789,876
%N Positive numbers all of whose pairs of consecutive decimal digits differ by 1.
%C Number of n-digit terms: 9, 17, 32, 61, 116, 222, 424 (= A090994).
%C Also called 10-esthetic numbers (where in general a q-esthetic number has the property that the consecutive digits of its base-q representation differ by 1, see "Esthetic numbers" by J. M. De Koninck and N. Doyon). - _Narad Rampersad_, Aug 03 2018
%H Reinhard Zumkeller, <a href="/A033075/b033075.txt">Table of n, a(n) for n = 1..10000</a>
%H J. M. De Koninck and N. Doyon, <a href="http://www.jeanmariedekoninck.mat.ulaval.ca/fileadmin/jmdk/Documents/Publications/2009_esthetic_numbers.pdf">Esthetic numbers</a>, Annales des Sciences mathématiques du Québec, 33 (2009), 155-164.
%F a(n) >> n^3.53267..., where the exponent is log 10/log k and k is the largest root of x^5 - x^4 - 4x^3 + 3x^2 + 3x - 1. - _Charles R Greathouse IV_, Mar 11 2014
%t Join[Range[9],Select[Range[2000],Union[Abs[Differences[IntegerDigits[#]]]]=={1}&]] (* _Harvey P. Dale_, Dec 28 2011 *)
%o (Haskell)
%o -- import Data.Set (fromList, deleteFindMin, insert)
%o a033075 n = a033075_list !! (n-1)
%o a033075_list = f (fromList [1..9]) where
%o f s | d == 0 = m : f (insert (10*m+1) s')
%o | d == 9 = m : f (insert (10*m+8) s')
%o | otherwise = m : f (insert (10*m+d-1) (insert (10*m+d+1) s'))
%o where (m,s') = deleteFindMin s
%o d = mod m 10
%o -- _Reinhard Zumkeller_, Feb 21 2012
%o (PARI) diff(v)=vector(#v-1,i,v[i+1]-v[i])
%o is(n)=if(n>9, Set(abs(diff(digits(n))))==[1], n>0) \\ _Charles R Greathouse IV_, Mar 11 2014
%o (Python)
%o def ok(n):
%o s = str(n)
%o return all(abs(int(s[i]) - int(s[i+1])) == 1 for i in range(len(s)-1))
%o print(list(filter(ok, range(1, 877)))) # _Michael S. Branicky_, Aug 22 2021
%o (Python) # faster version for initial segment of sequence
%o def gen(d, s=None): # generate remaining d digits, from start digit s
%o if d == 0:
%o yield tuple()
%o return
%o if s == None:
%o yield from [(i, ) + g for i in range(1, 10) for g in gen(d-1, s=i)]
%o else:
%o if s > 0:
%o yield from [(s-1, ) + g for g in gen(d-1, s=s-1)]
%o if s < 9:
%o yield from [(s+1, ) + g for g in gen(d-1, s=s+1)]
%o def agentod(digits):
%o for d in range(1, digits+1):
%o yield from [int("".join(map(str, g))) for g in gen(d, s=None)]
%o print(list(agentod(11))) # _Michael S. Branicky_, Aug 22 2021
%Y Cf. A090994, A048398 (primes), A048411 (squares), A207954 (palindromes).
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_
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